The school edition. Euclid's Elements of geometry, the first six books, by R. Potts. corrected and enlarged. corrected and improved [including portions of book 11,12]. |
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Side 57
... the one respectively equal to two sides of the other , and the contained angles
supplemental , the two triangles are equal . ... The square being considered as
an equilateral rectangle , its area or surface may be expressed numerically if the
...
... the one respectively equal to two sides of the other , and the contained angles
supplemental , the two triangles are equal . ... The square being considered as
an equilateral rectangle , its area or surface may be expressed numerically if the
...
Side 86
and through D , E , C , draw DK , EL , CH parallel to BG , meeting GH in K , L , H .
Then the rectangle BH is equal to the rectangles BK , DL , EH . And BH is
contained by A and BC , for it is contained by GB , BC , and GB is equal to A : and
the ...
and through D , E , C , draw DK , EL , CH parallel to BG , meeting GH in K , L , H .
Then the rectangle BH is equal to the rectangles BK , DL , EH . And BH is
contained by A and BC , for it is contained by GB , BC , and GB is equal to A : and
the ...
Side 87
THEOREM . if a straight line be dirided into any two parts , the rectangle
contained by the whole and one of the parts , is equal to the rectangle contained
by the two parts , together with the square on the aforesaid part . Let the straight
line AB ...
THEOREM . if a straight line be dirided into any two parts , the rectangle
contained by the whole and one of the parts , is equal to the rectangle contained
by the two parts , together with the square on the aforesaid part . Let the straight
line AB ...
Side 88
It is likewise rectangular ; for , since CG is parallel to BK , and B C meets them ,
therefore the angles KBC , BCG are equal ... and that AG is the rectangle
contained by AC , CB , for GC ' is equal to CB ; therefore GE is also equal to the
rectangle ...
It is likewise rectangular ; for , since CG is parallel to BK , and B C meets them ,
therefore the angles KBC , BCG are equal ... and that AG is the rectangle
contained by AC , CB , for GC ' is equal to CB ; therefore GE is also equal to the
rectangle ...
Side 89
therefore also AL is equal to DF ; to each of these equals add CH , and therefore
the whole AH is equal to DF and CH : but AH is the rectangle contained by AD ,
DB , for DH is equal to DB ; and DF together with CH is the gnomon CMG ...
therefore also AL is equal to DF ; to each of these equals add CH , and therefore
the whole AH is equal to DF and CH : but AH is the rectangle contained by AD ,
DB , for DH is equal to DB ; and DF together with CH is the gnomon CMG ...
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Vanlige uttrykk og setninger
ABCD Algebraically Apply base bisected Book chord circle circumference common construction contained definition demonstrated described diagonals diameter difference distance divided double draw drawn equal equal angles equiangular equilateral triangle equimultiples Euclid extremities fall figure formed four fourth Geometrical given circle given line given point given straight line greater half Hence inscribed intersection isosceles join length less Let ABC line drawn magnitudes manner mean meet multiple parallel parallelogram pass perpendicular plane problem produced Prop proportionals proved Q.E.D. PROPOSITION radius ratio reason rectangle rectangle contained regular remaining respectively right angles segment semicircle shew shewn sides similar solid square straight line taken tangent THEOREM third touch triangle ABC twice units vertex wherefore whole
Populære avsnitt
Side 112 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Side 83 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Side 48 - If two triangles have two sides of the one equal to two sides of the other, each to each ; and...
Side 238 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Side 198 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater, that is, ' when the less is contained a certain number of times exactly in the greater.
Side 271 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.
Side 81 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 115 - angle in a segment' is the angle contained by two straight lines drawn from any point in the circumference of the segment, to the extremities of the straight line which is the base of the segment.
Side 341 - On the same base, and on the same side of it, there cannot be two triangles...
Side 24 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.
Bibliografisk informasjon
| Tittel | The school edition. Euclid's Elements of geometry, the first six books, by R. Potts. corrected and enlarged. corrected and improved [including portions of book 11,12]. |
| Forfatter | Euclides |
| Redaktør | Robert Potts |
| Utgave | 5 |
| distribuert | 1864 |
| Original fra | Oxford University |
| Digitalisert | 7. sep 2006 |
| Eksporter sitat | BiBTeX EndNote RefMan |